1 / 8

By: Ryan Winters and Cameron Kerst

The Canadian Lynx vs. the Snowshoe Hare: The Predator-Prey Relationship and the Lotka-Volterra Model. By: Ryan Winters and Cameron Kerst. Photo Courtesy of http://taggart.glg.msu.edu/bs110/lynx1.gif. An Overview. The Canadian Lynx population fluctuates based upon the Snowshoe Hare population

bree
Download Presentation

By: Ryan Winters and Cameron Kerst

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The Canadian Lynx vs. the Snowshoe Hare: The Predator-Prey Relationship and the Lotka-Volterra Model By: Ryan Winters and Cameron Kerst Photo Courtesy of http://taggart.glg.msu.edu/bs110/lynx1.gif

  2. An Overview • The Canadian Lynx population fluctuates based upon the Snowshoe Hare population • Share a common habitat in the Boreal forests of Canada • All data comes from records of the Hudson Bay fur company

  3. Background of the Lotka-Volterra Model • Developed Simultaneously by Alfred J. Lotka and Vito Volterra • Volterra, an Italian professor of math, developed the model while trying to explain his son’s observations of fish predators. • Lotka, a chemist, demographer ecologist and mathematician, addressed the model in his book ElementsofPhysical Biology.

  4. Explaining the Model dH= aH(t)-bH(t)L(t) dL= cH(t)L(t)-eL(t) dt • dH/dt is Malthusian, depends : aH(t) • extension of the basic Verhulst (logistic) Model • Outputs rate at which the respective population in changing at time t • a=intrinsic rate of Hare population increase (births) • b=predation rate coefficient • c=reproduction rate of predators per 1 prey eaten • e=predator mortality rate dt

  5. Applying the Data • We chose values for our coefficients that best fit our population data graph • Also initial conditions were taken under consideration in order to most accurately depict our original data • This yielded these rate equations H’=0.7R(t)-1.25R(t)L(t) L’=R(t)L(t)-L(t) a=0.7 b=1.25 c=1 e=1

  6. IVP and the Model • After finding our rate equations we then formed an IVP with an initial conditions and rate equations • We used our coefficients that we found and used Euler’s Method to compare our model with the actual data I.C.= H(1900)=3* L(1900)=.4* *Population in thousands R.E.= H’= aH(t)-bH(t)L(t) L’= cH(t)L(t)-eL(t)

  7. Works Consulted • Works Consulted: • Lotka, Alfred J. ElementsofPhysicalBiology. • Mahaffy, Joseph M. “Lotka-Volterra Models.” San Diego State University: 2000. http://www- rohan.sdsu.edu/~jmahaffy/courses/f00/math122/lectures/qual_de2/qualde2.html • McKelvey, Steve. “Lotka-Volterra Two Species Model.” <http://www.stolaf.edu/people/mckelvey/envision.dir/lotka-volt.html > • Sharov, Alexei. “Lotka-Volterra Model.” 01/12/1996. < http://www.gypsymoth.ento.vt.edu/~sharov/PopEcol/lec10/lotka.html > • “Vito Voltera.” School of Mathematics and Statistics, University of St. Andrews, Scotland. December 1996. < http://www-groups.dcs.st- and.ac.uk/~history/Mathematicians/Volterra.html > • “Alfred J. Lotka.” Wikipedia. • <http://www.stolaf.edu/people/mckelvey/envision.dir/lotka-volt.html > 12/01/2005

  8. The End Thank You!!!

More Related